Problem: Rewrite as a simplified fraction. ${0.7\overline{3} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 73.3333...\\ 10x &= 7.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 66}$ ${x = \dfrac{66}{90}} $ ${x = \dfrac{11}{15}} $